Music Apps for the Moto X

The best one IMO is the Google Play Music, however Amazon's MP3 store is also available for Android. Otherwise you can import your own music library to your phone and there is a wide variety of different apps that can play your music.

If you're asking where to download music for free, nobody here will help you as it's against the TOS we all (including you) agreed to when signing up for the forum.

You can buy music from Google Play Music or the Amazon MP3 app. You can also subscribe to any number of streaming services such as Spoify, Pandora, Last.FM, etc. Google Play Music will also allow you to upload your collection to the "cloud" so you can stream it to any device.